Advertisement

Mathematische Zeitschrift

, Volume 122, Issue 2, pp 166–176 | Cite as

Demi-semi-primal algebras and Mal'cev-type conditions

  • Robert W. Quackenbush
Article

Keywords

Boolean Algebra Free Algebra Congruence Lattice Equational Class Direct Power 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Day, R. A.: A characterization of modularity for congruence lattices of algebras. Canadian Math. Bull.12, 167–173 (1969).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Day, R. A.: Injectivity in congruence distributive equational classes. Ph. D. Thesis, McMaster Univ., 1970.Google Scholar
  3. 3.
    Foster, A. L.: Families of algebras with unique (sub-)direct factorization: Equational characterization of factorization. Math. Ann.166, 302–326 (1966).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    —: Automorphisms and functional completeness in universal algebras. I. General automorphisms, Structure theory and characterization. Math. Ann.180, 138–169 (1969).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    — Pixley, A. F.: Semi-categorical algebras. I. Semi-primal algebras. Math. Z.83, 147–169 (1964).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    ——: Semi-categorical algebras. II. Math. Z.85, 169–184 (1964).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Fraser, G., Horn, A.: Congruence relations in direct products. Proc. Amer. Math. Soc.26, 390–394 (1970).MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Grätzer, G.: Universal algebra. Princeton, N.J.: D. Van Nostrand Co. 1968.zbMATHGoogle Scholar
  9. 9.
    —: Two Mal'cev-type theorems in universal algebra. J. Combinat. Theory8, 334–342 (1970).CrossRefzbMATHGoogle Scholar
  10. 10.
    Halmos, P. R.: Algebraic logic. New York: Chelsea Publishing Co. 1962.zbMATHGoogle Scholar
  11. 11.
    Jónsson, B.: Algebras whose congruence lattices are distributive. Math. Scandinav.21, 110–121 (1967).MathSciNetzbMATHGoogle Scholar
  12. 12.
    Mal'cev, A. I.: On the general theory of algebraic systems [Russian]. Mat. Sbornik, N.S.35, (77) 3–20 (1954).MathSciNetGoogle Scholar
  13. 13.
    Pixley, A. F.: Distributivity and permutability of congruence relations in equational classes of algebras. Proc. Amer. Math. Soc.14, 105–109 (1963).MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    —: Functionally complete algebras generating distributive and permutable classes. Math. Z.114, 361–372 (1970).MathSciNetCrossRefGoogle Scholar
  15. 15.
    Pixley, A. F.: The ternary discriminator function in universal algebra. Preprint.Google Scholar
  16. 16.
    Pixley, A. F.: Local Mal'cev conditions. To appear.Google Scholar
  17. 17.
    Wille, R.: Kongruenzklassengeometrien. Lecture Notes in Math. 113. Berlin-Heidelberg-New York: Springer 1970.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • Robert W. Quackenbush
    • 1
  1. 1.Department of MathematicsThe University of ManitobaWinnipegCanada

Personalised recommendations